Method and apparatus for avoiding register interference

ABSTRACT

The aspects enable a computing device to allocate memory space to variables during runtime compilation of a software application. A first variable associated with a code segment within code being compiled may be identified and assigned a priority tag. A second variable associated with another code segment within the code being compiled may also be assigned a priority tag. A determination may be made regarding whether the first and second variables are contemporaneously live during execution, and whether legal storage location sets for the first and second variables overlap. The assigned priority tags may be used for assigning storage locations to the first and second variables based on the determination.

BACKGROUND

Cellular and wireless communication technologies have seen explosivegrowth over the past several years. This growth has been fueled bybetter communications, hardware, larger networks, and more reliableprotocols. Wireless service providers are now able to offer theircustomers an ever-expanding array of features and services, and provideusers with unprecedented levels of access to information, resources, andcommunications. To keep pace with these service enhancements, mobileelectronic devices (e.g., cellular phones, tablets, laptops, etc.) havebecome more powerful and complex than ever. With this increase inprocessing speed, usage, and performance, there is an increased demandfor improving the efficiency and processing speed of the mobile devices,which may be achieved via faster and more sophisticated compilers andcompiling frameworks.

Generally, application software written for mobile computing devices iscompiled into executable code which is what users refer to as“applications.” Developers typically use a compiler to translate codewritten in higher level programming languages into executable codesuitable for target mobile computing devices. Application software maybe distributed as pure executable code, in which case the compiling stepis typically performed by the developer on what is referred to as a“static compiler.” Application software may also be written so portionsof the code are compiled at runtime using software modules within themobile computing device referred to as a “runtime compiler.” Runtimecompilers (e.g., dynamic compilers or Just in Time compilers) translatesegments of code into executable native code (e.g., machine code) at thetime the code is executed.

SUMMARY

The various aspects include methods of allocating storage locations tovariables while compiling code for a computing system, which may includeidentifying a first variable associated with a code segment within codebeing compiled, assigning a first priority tag to the first variable,identifying a second variable associated with another code segmentwithin the code being compiled, assigning a second priority tag to thesecond variable, and using the assigned priority tags in assigningstorage locations to the first and second variables. In an aspect, usingthe assigned priority tags in assigning storage locations to the firstand second variables includes determining whether the first and secondvariable are contemporaneously live during execution of the compiledcode, and determining whether legal storage location sets for the firstand second variables overlap when it is determined that the first andsecond variable are contemporaneously live during execution of thecompiled code. In a further aspect, using the assigned priority tags inassigning storage locations to the first and second variables furtherincludes using the assigned priority tags to either assign a new legalset of storage locations to one or both of the first and secondvariables or to determine that an interference edge should be added toan interference graph. In a further aspect, using the assigned prioritytags in assigning storage locations to the first and second variablesfurther includes comparing the priority tags assigned to each of thefirst and second variables when it is determined that the first andsecond variables are contemporaneously live during execution of thecompiled code and have overlapping legal storage location sets. In afurther aspect, the method includes inserting an interference edge in aninterference graph, and proceeding with compiler operations when thefirst and second variables both have low priority tags. In a furtheraspect, the method includes subtracting the legal storage location setof the higher priority variable from the legal storage location set toobtain a remainder set of storage locations when the first and secondvariables have different priority tags, determining whether theremainder set is empty, assigning the remainder set to the variable withthe lower priority tag as a new legal parameter set, and proceeding withthe compiler operations when the remainder set of storage locations isnot empty, and inserting an interference edge in an interference graph,and proceeding with the compiler operations when the remainder set ofstorage locations is empty. In a further aspect, the method includesdetermining an intersection set of legal storage locations common toboth the first and second variables when the first and second variablesboth have high priority tags, and partitioning the intersection set oflegal storage locations approximately equally between the first andsecond variables into a first partition set for the first variable and asecond partition set for the second variable. In a further aspect, themethod includes subtracting the first partition set from the legalpartition set of the second variable to obtain a first remainder set,subtracting the second partition set from the legal partition set of thefirst variable to obtain a second remainder set, determining whether thefirst remainder set is empty, and determining whether the secondremainder set is empty. In a further aspect, the method includesinserting an interference edge in an interference graph and proceedingwith the compiler operations when either of the first or secondremainder sets is empty. In a further aspect, the method includesassigning the first remainder set to the first variable as a new legalstorage location set, assigning the second remainder set to the firstvariable as a new legal storage location set, and proceeding with thecompiler operations when both of the first and second remainder sets arenot empty. In a further aspect, identifying a first variable associatedwith a code segment within code being compiled includes identifying afirst variable associated with a code segment within code being compiledby a runtime compiler. In a further aspect, identifying a first variableassociated with a code segment within code being compiled includesidentifying a first variable associated with a code segment within codebeing compiled by a static compiler.

Further aspects include a computing device configured to allocatestorage locations to variables while compiling code that includes amemory, a processor, means for identifying a first variable associatedwith a code segment within code being compiled, means for assigning afirst priority tag to the first variable, means for identifying a secondvariable associated with another code segment within the code beingcompiled, means for assigning a second priority tag to the secondvariable, and means for using the assigned priority tags in assigningstorage locations to the first and second variables. In an aspect, meansfor using the assigned priority tags in assigning storage locations tothe first and second variables includes means for determining whetherthe first and second variable are contemporaneously live duringexecution of the compiled code, and means for determining whether legalstorage location sets for the first and second variables overlap when itis determined that the first and second variable are contemporaneouslylive during execution of the compiled code. In a further aspect, meansfor using the assigned priority tags in assigning storage locations tothe first and second variables further includes means for using theassigned priority tags to either assign a new legal set of storagelocations to one or both of the first and second variables or todetermine that an interference edge should be added to an interferencegraph. In a further aspect, means for using the assigned priority tagsin assigning storage locations to the first and second variables furtherincludes means for comparing the priority tags assigned to each of thefirst and second variables when it is determined that the first andsecond variables are contemporaneously live during execution of thecompiled code and have overlapping legal storage location sets. In afurther aspect, the computing device includes means for inserting aninterference edge in an interference graph and proceeding with compileroperations when the first and second variables both have low prioritytags. In a further aspect, the computing device includes means forsubtracting the legal storage location set of the higher priorityvariable from the legal storage location set to obtain a remainder setof storage locations when the first and second variables have differentpriority tags, means for determining whether the remainder set is empty,means for assigning the remainder set to the variable with the lowerpriority tag as a new legal parameter set and proceeding with thecompiler operations when the remainder set of storage locations is notempty, and means for inserting an interference edge in an interferencegraph and proceeding with the compiler operations when the remainder setof storage locations is empty. In a further aspect, the computing deviceincludes means for determining an intersection set of legal storagelocations common to both the first and second variables when the firstand second variables both have high priority tags, and means forpartitioning the intersection set of legal storage locationsapproximately equally between the first and second variables into afirst partition set for the first variable and a second partition setfor the second variable. In a further aspect, the computing deviceincludes means for subtracting the first partition set from the legalpartition set of the second variable to obtain a first remainder set,means for subtracting the second partition set from the legal partitionset of the first variable to obtain a second remainder set, means fordetermining whether the first remainder set is empty, and means fordetermining whether the second remainder set is empty. In a furtheraspect, the computing device includes means for inserting aninterference edge in an interference graph and proceeding with thecompiler operations when either of the first or second remainder sets isempty. In a further aspect, the computing device includes means forassigning the first remainder set to the first variable as a new legalstorage location set, means for assigning the second remainder set tothe first variable as a new legal storage location set, and means forproceeding with the compiler operations when both of the first andsecond remainder sets are not empty. In a further aspect, means foridentifying a first variable associated with a code segment within codebeing compiled includes means for identifying a first variableassociated with a code segment within code being compiled by a runtimecompiler. In a further aspect, means for identifying a first variableassociated with a code segment within code being compiled includes meansfor identifying a first variable associated with a code segment withincode being compiled by a static compiler.

Further aspects include a non-transitory computer readable storagemedium having stored thereon processor-executable software instructionsconfigured to cause a processor to perform operations for allocatingstorage locations to variables while compiling code, the operationsincluding identifying a first variable associated with a code segmentwithin code being compiled, assigning a first priority tag to the firstvariable, identifying a second variable associated with another codesegment within the code being compiled, assigning a second priority tagto the second variable, and using the assigned priority tags inassigning storage locations to the first and second variables. In anaspect, the stored processor-executable instructions are configured tocause a processor to perform operations such that using the assignedpriority tags in assigning storage locations to the first and secondvariables includes determining whether the first and second variable arecontemporaneously live during execution of the compiled code, anddetermining whether legal storage location sets for the first and secondvariables overlap when it is determined that the first and secondvariable are contemporaneously live during execution of the compiledcode. In a further aspect, the stored processor-executable instructionsare configured to cause a processor to perform operations such thatusing the assigned priority tags in assigning storage locations to thefirst and second variables further includes using the assigned prioritytags to either assign a new legal set of storage locations to one orboth of the first and second variables or to determine that aninterference edge should be added to an interference graph. In a furtheraspect, the stored processor-executable instructions are configured tocause a processor to perform operations such that using the assignedpriority tags in assigning storage locations to the first and secondvariables further includes comparing the priority tags assigned to eachof the first and second variables when it is determined that the firstand second variables are contemporaneously live during execution of thecompiled code and have overlapping legal storage location sets. In afurther aspect, the stored processor-executable instructions areconfigured to cause a processor to perform operations further includinginserting an interference edge in an interference graph and proceedingwith compiler operations when the first and second variables both havelow priority tags. In a further aspect, the stored processor-executableinstructions are configured to cause a processor to perform operationsfurther including subtracting the legal storage location set of thehigher priority variable from the legal storage location set to obtain aremainder set of storage locations when the first and second variableshave different priority tags, determining whether the remainder set isempty, assigning the remainder set to the variable with the lowerpriority tag as a new legal parameter set and proceeding with thecompiler operations when the remainder set of storage locations is notempty, and inserting an interference edge in an interference graph andproceeding with the compiler operations when the remainder set ofstorage locations is empty. In a further aspect, the storedprocessor-executable instructions are configured to cause a processor toperform operations further including determining an intersection set oflegal storage locations common to both the first and second variableswhen the first and second variables both have high priority tags, andpartitioning the intersection set of legal storage locationsapproximately equally between the first and second variables into afirst partition set for the first variable and a second partition setfor the second variable. In a further aspect, the storedprocessor-executable instructions are configured to cause a processor toperform operations further including subtracting the first partition setfrom the legal partition set of the second variable to obtain a firstremainder set, subtracting the second partition set from the legalpartition set of the first variable to obtain a second remainder set,determining whether the first remainder set is empty, and determiningwhether the second remainder set is empty. In a further aspect, theprocessor is configured with processor-executable instructions toperform operations further including inserting an interference edge inan interference graph, and proceeding with the compiler operations wheneither of the first or second remainder sets is empty. In a furtheraspect, the stored processor-executable instructions are configured tocause a processor to perform operations further including assigning thefirst remainder set to the first variable as a new legal storagelocation set, assigning the second remainder set to the first variableas a new legal storage location set, and proceeding with the compileroperations when both of the first and second remainder sets are notempty. In a further aspect, the stored processor-executable instructionsare configured to cause a processor to perform operations such thatidentifying a first variable associated with a code segment within codebeing compiled includes identifying a first variable associated with acode segment within code being compiled by a runtime compiler. In afurther aspect, the stored processor-executable instructions areconfigured to cause a processor to perform operations such thatidentifying a first variable associated with a code segment within codebeing compiled includes identifying a first variable associated with acode segment within code being compiled by a static compiler.

Further aspects include a computing device, including a memory, and aprocessor coupled to the receiver and the memory, wherein the processoris configured with processor-executable instructions to performoperations including identifying a first variable associated with a codesegment within code being compiled, assigning a first priority tag tothe first variable, identifying a second variable associated withanother code segment within the code being compiled, assigning a secondpriority tag to the second variable, and using the assigned prioritytags in assigning storage locations to the first and second variables.In an aspect, the processor is configured with processor-executableinstructions to perform operations such that using the assigned prioritytags in assigning storage locations to the first and second variablesincludes determining whether the first and second variable arecontemporaneously live during execution of the compiled code, anddetermining whether legal storage location sets for the first and secondvariables overlap when it is determined that the first and secondvariable are contemporaneously live during execution of the compiledcode. In a further aspect, the processor is configured withprocessor-executable instructions to perform operations such that usingthe assigned priority tags in assigning storage locations to the firstand second variables further includes using the assigned priority tagsto either assign a new legal set of storage locations to one or both ofthe first and second variables or to determine that an interference edgeshould be added to an interference graph. In a further aspect, theprocessor is configured with processor-executable instructions toperform operations such that using the assigned priority tags inassigning storage locations to the first and second variables furtherincludes comparing the priority tags assigned to each of the first andsecond variables when it is determined that the first and secondvariables are contemporaneously live during execution of the compiledcode and have overlapping legal storage location sets. In a furtheraspect, the processor is configured with processor-executableinstructions to perform operations further including inserting aninterference edge in an interference graph and proceeding with compileroperations when the first and second variables both have low prioritytags. In a further aspect, wherein the processor is configured withprocessor-executable instructions to perform operations furtherincluding subtracting the legal storage location set of the higherpriority variable from the legal storage location set to obtain aremainder set of storage locations when the first and second variableshave different priority tags, determining whether the remainder set isempty, assigning the remainder set to the variable with the lowerpriority tag as a new legal parameter set and proceeding with thecompiler operations when the remainder set of storage locations is notempty, and inserting an interference edge in an interference graph andproceeding with the compiler operations when the remainder set ofstorage locations is empty. In a further aspect, the processor isconfigured with processor-executable instructions to perform operationsfurther including determining an intersection set of legal storagelocations common to both the first and second variables when the firstand second variables both have high priority tags, and partitioning theintersection set of legal storage locations approximately equallybetween the first and second variables into a first partition set forthe first variable and a second partition set for the second variable.In a further aspect, the processor is configured withprocessor-executable instructions to perform operations furtherincluding subtracting the first partition set from the legal partitionset of the second variable to obtain a first remainder set, subtractingthe second partition set from the legal partition set of the firstvariable to obtain a second remainder set, determining whether the firstremainder set is empty, and determining whether the second remainder setis empty. In a further aspect, the processor is configured withprocessor-executable instructions to perform operations furtherincluding inserting an interference edge in an interference graph andproceeding with the compiler operations when either of the first orsecond remainder sets is empty. In a further aspect, the processor isconfigured with processor-executable instructions to perform operationsfurther including assigning the first remainder set to the firstvariable as a new legal storage location set, assigning the secondremainder set to the first variable as a new legal storage location set,and proceeding with the compiler operations when both of the first andsecond remainder sets are not empty. In a further aspect, the processoris configured with processor-executable instructions such thatidentifying a first variable associated with a code segment within codebeing compiled includes identifying a first variable associated with acode segment within code being compiled by a runtime compiler. In afurther aspect, the processor is configured with processor-executableinstructions such that identifying a first variable associated with acode segment within code being compiled includes identifying a firstvariable associated with a code segment within code being compiled by astatic compiler.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated herein and constitutepart of this specification, illustrate exemplary embodiments of theinvention, and together with the general description given above and thedetailed description given below, serve to explain the features of theinvention.

FIG. 1 is an architectural diagram illustrating information flows in acomputing system suitable for implementing the various aspects.

FIG. 2 is an illustration of an example interference graph suitable foruse with the various aspects.

FIGS. 3-4 are process flow diagrams of aspect methods for improving theefficiency, speed, and overall performance of a compiler.

FIG. 5 is a component block diagram of a mobile device suitable for usewith the various aspects.

FIG. 6 is a component block diagram of a work station suitable for usewith the various aspects.

DETAILED DESCRIPTION

The various aspects will be described in detail with reference to theaccompanying drawings. Wherever possible, the same reference numberswill be used throughout the drawings to refer to the same or like parts.References made to particular examples and implementations are forillustrative purposes, and are not intended to limit the scope of theinvention or the claims.

The word “exemplary” is used herein to mean “serving as an example,instance, or illustration.” Any implementation described herein as“exemplary” is not necessarily to be construed as preferred oradvantageous over other implementations.

The terms “mobile device” and “receiver device” are used interchangeablyherein to refer to any one or all of cellular telephones, smartphones,personal or mobile multi-media players, personal data assistants(PDA's), laptop computers, tablet computers, smartbooks, palm-topcomputers, wireless electronic mail receivers, multimedia Internetenabled cellular telephones, wireless gaming controllers, and similarpersonal electronic devices which include a memory, a programmableprocessor for which performance is important, and operate under batterypower such that power conservation methods are of benefit. While thevarious aspects are particularly useful for compiling applications runon mobile computing devices, such as smartphone, which have limitedmemory and processing power, the aspects are generally useful in anycompiler used to compile application software for computing devices thatinclude a processor and execute application programs.

The phrases “legal set” and “legal register set” are usedinterchangeably herein to refer to a set of registers in the computingdevice which a particular variable is allowed to use. Some operationsmay place restrictions on the types or identity of registers that may beused, while other operations may place no restrictions on the registers(i.e., any available register may be used).

The various aspects provide compiler methods for preventing code segmentvariables (referred to as “values” or “value data structures”) fromcompeting for the same storage locations and for managing value-registerconflicts. Various aspects implement methods that generate smaller andmore efficient interference graphs for all instruction setarchitectures, including those which do not include instructions thatare limited to a single register (e.g., ARM). Various aspects generateinterference graphs having a reduced number of interference edges, whichreduces memory usage and improves the speed of execution of the compilersoftware.

Register allocation is a compiler process that assigns variables tohardware registers during program execution. Assigning variables tohardware registers is an important compiler optimization because adevice processor is able to access variables assigned to hardwareregisters much faster than variables stored in non-register memories. Itis common for a compiler process to generate more variables than thereare available hardware registers on a typical mobile computing device.To address such scenarios, multiple variables may be assigned to asingle register and/or the variables may be “spilled” to (i.e., storedin) alternative locations, such as cache memory, disk storage, etc.These operations add computational complexities to the compiler processof assigning the variables to hardware registers and reduce the overallspeed of the computing device by increasing the overall compile time ofthe runtime compiler and by increasing the runtime of the generatedcode. That is, since the runtime compiler performs these compileoperations during the program's execution, such increases in compiletime greatly impact the user experience by occupying and slowing downthe mobile device processors. The various aspects provide improvedregister allocation techniques that significantly reduce the overallcompile time and greatly improve the efficiency and performance ofmobile device processors.

Generally, register allocation processes allocate variables to hardwareregisters by implementing graph coloring methodologies that utilizeinterference graphs. An interference graph is a data-structure that maybe used to determine the safety of certain software operations, andidentify conflicts between two or more virtual registers. Specifically,interference graphs enable the runtime compiler to identify situationsin which two or more values are likely to compete for storage at thesame time (i.e., are alive at the same time) and manage the allocationof these values accordingly.

Due to the above-mentioned computational complexities, existing registerallocation solutions may result in large and complex interferencegraphs. Since the runtime compiler allocates the registers at runtime(e.g., during the execution of an application program), the amount oftime required to construct and manipulate these complex graphs maybecome prohibitive by driving up the total compilation time. The variousaspects reduce the total compilation time by constructing and tuninginterference graphs efficiently. The various aspects minimize the sizeand complexity of the interference graphs utilized by the registerallocation processes. These smaller and more efficient interferencegraphs enable the runtime compiler to allocate registers faster and moreefficiently, reducing the overall compile time and improving processorperformance.

The various aspects may be implemented in a wide variety of systems andarchitectures, an example of which is illustrated in FIG. 1.Specifically, FIG. 1 illustrates information flows through an examplevirtual machine 108 of a computing system 100 suitable for implementingthe various aspects. In the illustrated example, when a computer programis executed, source code 102 written in a high level language isprovided to a compiler module 104 within a compile-time environment 120,which translates the source code 102 into a virtual instruction setarchitecture (Virtual ISA code) and/or byte code 106. The source code102 may be translated into the byte code 106 at the time source code 102is created by a software developer. The generated byte code 106 may begenerated such that it may be distributed to a wide variety of mobiledevices having different platforms and execution environments, so longas the mobile devices supports the ISA used to generate the bytecode 106(i.e., the generated byte code 106 may be platform independent).

The computing system 100 may also include a runtime environment 122 thatincludes a virtual machine 108 and an operating system 116. The virtualmachine 108 may be a software application that executes applicationprograms like a physical hardware machine. The virtual machine 108 mayprovide an interface between the application programs and the physicalhardware, potentially allowing application programs tied to a specificinstruction set architecture (ISA) to execute on hardware implementing adifferent instruction set architecture. In the illustrated example ofFIG. 1, the virtual machine 108 includes a runtime compiler 110, aninterpreter 112, and a runtime system 114.

Byte code 106 generated by the compile time environment 120 may beprovided to the either the runtime compiler 110 or the interpreter 112of the virtual machine 108. If the byte code 106 is provided to thecompiler 110, the methods and procedures stored by the byte codes may becompiled into machine instructions, whereas if the byte code 106 isprovided to the interpreter 112, the byte code may be read and executed“as is.” Thus, when requests (e.g., method calls) are issued to theoperating system 116, the runtime system 114 may determine whether therequest requires an interpreted method or a compiled method. If acompiled method is required, the runtime system 114 may activate theruntime compiler 110, which compiles the received byte code 106 togenerate, at runtime, an optimized set of machine instructions for theexecution. As part of these operations, the runtime compiler 110 mayperform register allocation operations that assign variables to thephysical hardware registers, which in existing solutions requires eitherthe generation of large and complex interference graphs or the use ofspecific instruction sets (e.g., (e.g., x86 or IA-32 microprocessorarchitecture) that include a large number of operations that operate ona single register, which is discussed in detail further below.

FIG. 2 illustrates an example interference graph 200 suitable for usewith the various aspects. As mentioned above, a register allocatormodule may control the use of registers within an optimized or otherwisecompiled program by allocating the register space in which dataassociated with the program may be stored. A register is a locationassociated with a processor that may be accessed faster than the othermemories (e.g., stack, heap, etc.) available to the processor. Toallocate such registers, the register allocator module may generate aninterference graph, which is a data-structure that provides arepresentation of the live ranges of the variables associated with aparticular portion of code. A live range is a range in a portion of codeover which a particular variable or value must remain accessible andavailable for use.

The interference graph 200 identifies conflicts between virtualregisters through the use of nodes 202, colors, and edges 204. Eachvirtual register may be represented by a node 202 in the graph (e.g.,nodes a-h), and physical registers may be represented by a color (notillustrated). If two virtual registers are both live (i.e., are bothbeing operated on) at the same point in the program, their nodes may beconnected with an edge 204. Thus, the nodes 202 in the graph mayrepresent values that need storage locations (registers), and the edges204 may represent scenarios in which two nodes need a storage locationat the same time (i.e., their live ranges overlap). If two variables donot interfere (i.e., there is no edge between their respective nodes inthe interference graph), then the same register may be used for bothvariables (e.g., for nodes a and g), reducing the number of registersneeded. If two nodes are adjacent (e.g., nodes a and c) due to thesharing of an edge 204, the live ranges of the variables overlap, andthe register allocator module may determine that each of these variablesshould be assigned a different color (and thus allocated to differentphysical register) than the other variables.

As mentioned above, edges between two nodes in the interference graphindicate that the two nodes interfere, and that the variables associatedwith the two nodes may not be stored in the same register. As the numberof edges increases, the interference graph grows larger and morecomplex. For example, in a typical bit-set implementation, theinterference graph may have thousands of edges and each edge may requireeight bytes of storage. In addition, the process of creating andmodifying these interference graphs may encompass a substantial part ofan overall compilation process.

The size and complexity of the interference graphs may be reduced byexploiting the features of certain instruction set architectures. Forexample, in some instruction set architectures (e.g., x86 or IA-32microprocessor architecture), certain operations only operate on asingle register. An example of this is the divide instruction in the x86instruction set, which is only capable of producing a result in the EAX(a register on the IA-32 microprocessor architecture). Since the resultsof the divide operation cannot be stored in any register other than theEAX register, whenever a program includes a divide instruction, theregister allocator may conclude that the EAX register is effectivelyoccupied and the other values should not have access to EAX register.

On such systems, two values only compete with one another if they arealive at the same time and can use exactly the same registers. Forexample, on x86 systems, floating-point operations must operate out ofthe floating-point registers and the integer operations must operate outof the integer registers. Therefore, a floating-point operation cannotinterfere with an integer operation because they can't be performed fromthe same registers, and those two values will never compete for the sameregister. As such, when generating the interference graph, the compilermay improve the device's runtime performance by reducing the number ofinterferences (edges), which may be achieved on the above-mentionedinstruction set architectures (e.g., x86 or IA-32 microprocessorarchitecture), by acknowledging that interferences will only exist ifthe live ranges overlap and the set of legal registers that the valuecould be placed in overlap.

In the presence of operations that must use a specific register (e.g.,x86 divide operations that must use the EAX register), instead ofdetermining whether the divide operation interferes with everything elsethat can be done in the any of the general-purpose registers, thecompiler may evaluate the live ranges by first subtracting the EAXregister from the legal set of available registers. In this manner, thecompiler may reduce the number of edges in the interference graph byacknowledging that (since the divide instruction must have access to getEAX register) such operations ought to be pre-colored to the EAXregister, and that EAX register should be removed from consideration(i.e., all non-divide operations should be mapped to registers otherthan EAX). By subtracting such registers from consideration, the totalnumber of edges in the interference graph may be reduced by a factor ofthree, and since the speed of the register allocator is directlyproportional to the number of edges in the interference graph, processorperformance is also improved by a factor of three.

Unlike the instruction set architectures described above (e.g., x86),some instruction set architectures (e.g., ARM) do not include very manyinstructions that are limited to a single register. For example, in ARMarchitectures, the instruction set is very “regular” and almost everyoperation may use exactly the same sets of registers as every otheroperation. In such architectures (e.g., ARM), the above mentionedtechniques for subtracting registers that are legal for a singleoperation (e.g., divide) from the universe of legal registers prior tothe allocation of registers is not as effective as they are on otherarchitectures (e.g., x86), because there are not as many registers thatmay be subtracted.

The various aspects implement methods that generate smaller and moreefficient interference graphs for all instruction set architectures,including those which do not include instructions that are limited to asingle register (e.g., ARM). Various aspects provide compiler methodsfor preventing code segment variables (referred to as “values” or “valuedata structures”) from competing for the same storage locations and formanaging value-register conflicts. Various aspects generate interferencegraphs having a reduced number of interference edges, which reducesmemory usage and improves the speed of the register allocator.

FIG. 3 illustrates an aspect method 300 for assigning priorities tovalues and generating an interference graph having a reduced number ofedges. In block 302, the runtime environment may receive all thevariables/values data structures that require an assignment. In block304, a tag field that specifies a priority (e.g., high, low, etc.) maybe added to each of the received value data structures. This prioritymay reflect the importance or frequency of the value to operations beingcompiled. The priority tag may also identify value data structure thatmust be loaded or processed in a particular register (i.e., lacksflexibility in terms of register assignments). Thus, it should beunderstood that the assignments of priority to variables or value datastructures may be accomplished using any of a variety of criteria,examples of which include: assigning a high priority tag to values thatare used frequently throughout execution of the code, if the value isnecessary for subsequent operations, the value is associated with acritical path or pacing operation (i.e., if it is held up the entireexecution is held up), and if the value must be place in a particularone or few registers due to the type of operation.

Returning to FIG. 3, in block 306, live analysis operations may beperformed to determine which values are live at which points in theprogram (e.g., to identify the live ranges). In determination block 307,it may be determined whether the live ranges of the variables overlap.If it is determined that two values are not live at the same time(determination block 307=“No”), in block 306, live analysis operationsmay continue until all the received data has been evaluation.

As mentioned above, two values only compete with one another if they arealive at the same time and can be stored in the same type of registers(share a legal set of locations). Thus, if it is determined that two ormore values are live at the same time (determination block 307=“Yes”),in block 308, the legal set of locations (i.e., register assignments)for each of the identified values may be compared to identify potentialinterferences or conflicts. In determination block 309, it may bedetermined whether the legal sets of locations for the variablesoverlap. In the event that the legal sets of value data structuresoverlap, the priority tags of those values may be compared. For example,if it is determined that the two legal sets overlap (determination block309=“Yes”), in block 310 the assigned tags may be compared to identifythe priority associated with each value.

If both values are low priority, the method inserts an interference edgein the interference graph data structure. If one of the value datastructures is tagged as high priority and the other value data structureis tagged as low priority, the method subtracts the set of legallocations of the high priority value from the set of legal locations forthe low priority value.

In block 312, the compiler may generate the interference graph using thepriority values. For example, if the compiler determines that bothvalues have a low priority, an interference edge may be inserted intothe graph. If one value has a higher priority than the other, the set oflegal locations of the higher priority value may be subtracted from theset of legal locations for the lower priority value. If as a result ofthis subtraction the remaining set is not empty, the remainder becomesthe new legal set for the low priority value, and no interference edgeis necessary. On the other hand, if the result of the subtraction isthat the set is empty, the method inserts an interference edge into theinterference graph, and leaves the legal sets unchanged. This leaves theinterference to be resolved in the ordinary manner of compilers. In theevent that both values are tagged as high priority, the method takes theintersection of legal sets for both value data structures, and thenpartitions that intersection into sets of roughly even size, andsubtracts one partition from one value, and the other partition from theother. If either new legal set becomes empty as a result of thissubtraction operation, then the method inserts an interference edge andleaves the legal sets unchanged. This relegates resolution to theordinary methods of the compiler. If both new sets are not empty as aresult of this subtraction, then the method uses the new legal sets, andno interference is necessary. Compilation of the code then proceeds inthe ordinary manner.

FIG. 4 illustrates an aspect method 400 for processing data valuestructures for generating an interference graph having a reduced numberof edges. In block 402, the compiler may perform live analysisoperations to identify the live ranges, and if two or more values arelive at the same time compare the legal set of locations (i.e., registerassignments) for each of the identified values to identify potentialinterferences or conflicts, similar to blocks 302-309 illustrated inFIG. 3. If the legal sets do not overlap (determination block 406=“No”),in block 402, the remaining portions of the code are evaluated. If thelegal sets overlap (determination block 406=“Yes”), in block 408 thepriority tags of those values may be compared to identify the priorityassociated with each value structure.

If, in block 408, the compiler determines that both values have a lowpriority, in block 410 an interference edge may be inserted into thegraph. However, if in block 408 the compiler determines that one valuehas a higher priority than the other, in block 412 the set of legallocations of the higher priority value may be subtracted from the set oflegal locations for the lower priority value. In determination block414, the compiler may determine whether, as a result of thissubtraction, the remaining set is empty or not. If the remaining set isempty (determination step 414=“Yes”), in block 410, the compiler insertsan interference edge into the interference graph, and leaves the legalsets unchanged. This leaves the interference to be resolved in theordinary manner of compilers. If, on the other hand, the remaining setis not empty (determination step 414=“No”), in block 416, the remainderbecomes the new legal set for the low priority value and no interferenceedge is necessary.

If, in block 408, the compiler determines that both values are tagged ashigh priority, in block 418, the complier may select the intersection oflegal sets for both value data structures. In block 420, the compliermay partition the intersection into sets of roughly even size. In block422, the complier may subtract one partition from one value and subtractthe other partition from the other value. In determination block 424,the compiler may determine if either new legal set will be empty as aresult of the subtraction operation. If the legal set is empty(determination block 424=“Yes”), in block 410, the compiler may insertan interference edge and leave the legal sets unchanged. This relegatesresolution to the ordinary methods of the compiler. If, on the otherhand, both new sets are not empty as a result of the subtractionoperation (determination block 424=“No”), in block 426 the compiler mayuse the new legal sets and determine that no interference is necessary.Compilation of the code then proceeds in the ordinary manner.

In block 428, the operations of the aspect method 400 may be repeatedfor additional values or the compiler operations may continue. It shouldbe understood that the processes of identifying contemporaneous values,determining whether overlaps exist, and addressing overlaps in the valueregister legal sets may be accomplished in a combined process. Thevarious aspect processes may also include one or more loops enabling theprocess to address all value data structures within the compiled code.Some of such loops are illustrated, but more complicated and recursiveloops may be implemented than illustrated.

While the above description evaluates just two levels of priority (i.e.,high and low), in an aspect, multiple levels of priority (e.g.,high/medium/low, scale of 1 to 5, etc.) may be used. In an aspect,multiple levels of priority may be implemented by executing the relativetests and allocations in sequence (e.g., such as high trumps medium andlow, and medium trumps low, etc.).

It should be appreciated that the assignment of priority tags to valuedata structures may be made at the time the value is identified in thecompilation process, and not at the end of processes that identifyvalues. Thus, the steps of tagging values may be accomplished throughoutearly passes of the compiler, and not just prior to identifying andresolving interferences. It should also be appreciated that theprocesses of identifying and addressing overlaps in the value registerlegal sets may be accomplished as contemporaneous values are identified,and not in a combined process.

One of the advantages of the aspects discussed herein is that they allowthe compiler developer to choose which types of values get advantaged inthe comparisons made in the register to value allocation process, whilesimultaneously decreasing the size of the interference graph, andspeeding up the compiler. For instance the compiler writer can identifyvalues which are defined or used by specific instructions to be highpriority, and therefore to get preferred access to the locations thatthey want.

Typical mobile devices 500 suitable for use with the various aspectswill have in common the components illustrated in FIG. 5. For example,an exemplary mobile receiver device 500 may include a processor 551coupled to internal memory 552, a display 550, and to a speaker 556.Additionally, the mobile device 500 may have an antenna 554 for sendingand receiving electromagnetic radiation that is connected to a mobilemultimedia receiver 555 coupled to the processor 551. In some aspects,the mobile multimedia receiver 555 may include an internal processor,such as a digital signal processor (DSP) for controlling operations ofthe receiver 555 and communicating with the device processor 551. Mobiledevices typically also include a key pad or miniature keyboard and menuselection buttons or rocker switches for receiving user inputs.

The processor 551 may be any programmable microprocessor, microcomputeror multiple processor chip or chips that can be configured byprocessor-executable software instructions (applications) to perform avariety of functions, including the functions of the various aspectsdescribed herein. Typically, software applications andprocessor-executable instructions may be stored in the internal memory552 before they are accessed and loaded into the processor 551. Theprocessor 551 may include internal memory sufficient to store theapplication software instructions. In some mobile devices, a securememory 556 may be in a separate memory chip coupled to the processor551. In many mobile devices 500, the internal memory 552 may be avolatile or nonvolatile memory, such as flash memory, or a mixture ofboth. For the purposes of this description, a general reference tomemory refers to all memory accessible by the processor 551, includinginternal memory 552, removable memory plugged into the mobile device,and memory within the processor 551 itself.

The various aspects involving static compilers may be implemented on anyof a variety of commercially available computers, servers and/or workstations, such as the work station 600 illustrated in FIG. 6. Such awork station 600 typically includes a processor 601 coupled to volatilememory 602 and a large capacity nonvolatile memory, such as a disk drive603. The work station 600 may also include a floppy disc drive, compactdisc (CD) or DVD disc drive 604 coupled to the processor 601. The workstation 600 may also include network access ports 606 coupled to theprocessor 601 for establishing data connections with a network 612, suchas a local area network coupled to other broadcast system computers andservers. Work stations 600 may also include operator interfaces, such asa keyboard 608, pointer device (e.g., a computer mouse 610), and adisplay 609.

The foregoing method descriptions and the process flow diagrams areprovided merely as illustrative examples and are not intended to requireor imply that the steps of the various aspects must be performed in theorder presented. As will be appreciated by one of skill in the art theorder of steps in the foregoing aspects may be performed in any order.Words such as “thereafter,” “then,” “next,” etc. are not intended tolimit the order of the steps; these words are simply used to guide thereader through the description of the methods. Further, any reference toclaim elements in the singular, for example, using the articles “a,”“an” or “the” is not to be construed as limiting the element to thesingular.

The various illustrative logical blocks, modules, circuits, andalgorithm steps described in connection with the aspects disclosedherein may be implemented as electronic hardware, computer software, orcombinations of both. To clearly illustrate this interchangeability ofhardware and software, various illustrative components, blocks, modules,circuits, and steps have been described above generally in terms oftheir functionality. Whether such functionality is implemented ashardware or software depends upon the particular application and designconstraints imposed on the overall system. Skilled artisans mayimplement the described functionality in varying ways for eachparticular application, but such implementation decisions should not beinterpreted as causing a departure from the scope of the presentinvention.

The hardware used to implement the various illustrative logics, logicalblocks, modules, and circuits described in connection with the aspectsdisclosed herein may be implemented or performed with a general purposeprocessor, a digital signal processor (DSP), a DSP within a multimediabroadcast receiver chip, an application specific integrated circuit(ASIC), a field programmable gate array (FPGA) or other programmablelogic device, discrete gate or transistor logic, discrete hardwarecomponents, or any combination thereof designed to perform the functionsdescribed herein. A general-purpose processor may be a microprocessor,but, in the alternative, the processor may be any conventionalprocessor, controller, microcontroller, or state machine. A processormay also be implemented as a combination of computing devices, e.g., acombination of a DSP and a microprocessor, a plurality ofmicroprocessors, one or more microprocessors in conjunction with a DSPcore, or any other such configuration. Alternatively, some steps ormethods may be performed by circuitry that is specific to a givenfunction.

In one or more exemplary aspects, the functions described may beimplemented in hardware, software, firmware, or any combination thereof.If implemented in software, the functions may be stored on ortransmitted over as one or more instructions or code on acomputer-readable medium. The steps of a method or algorithm disclosedherein may be embodied in a processor-executable software module whichmay reside on a computer-readable medium. Computer-readable mediaincludes both computer storage media and communication media includingany medium that facilitates transfer of a computer program from oneplace to another. A storage media may be any available media that may beaccessed by a computer. By way of example, and not limitation, suchcomputer-readable media may comprise RAM, ROM, EEPROM, CD-ROM or otheroptical disk storage, magnetic disk storage or other magnetic storagedevices, or any other medium that may be used to carry or store desiredprogram code in the form of instructions or data structures and that maybe accessed by a computer. Also, any connection is properly termed acomputer-readable medium. For example, if the software is transmittedfrom a website, server, or other remote source using a coaxial cable,fiber optic cable, twisted pair, digital subscriber line (DSL), orwireless technologies such as infrared, radio, and microwave, then thecoaxial cable, fiber optic cable, twisted pair, DSL, or wirelesstechnologies such as infrared, radio, and microwave are included in thedefinition of medium. Disk and disc, as used herein, includes compactdisc (CD), laser disc, optical disc, digital versatile disc (DVD),floppy disk, and blu-ray disc where disks usually reproduce datamagnetically, while discs reproduce data optically with lasers.Combinations of the above should also be included within the scope ofcomputer-readable media. Additionally, the operations of a method oralgorithm may reside as one or any combination or set of codes and/orinstructions on a machine readable medium and/or computer-readablemedium, which may be incorporated into a computer program product.

The preceding description of the disclosed embodiments is provided toenable any person skilled in the art to make or use the presentinvention. Various modifications to these embodiments will be readilyapparent to those skilled in the art, and the generic principles definedherein may be applied to other embodiments without departing from thespirit or scope of the invention. Thus, the present invention is notintended to be limited to the embodiments shown herein but is to beaccorded the widest scope consistent with the following claims and theprinciples and novel features disclosed herein.

What is claimed is:
 1. A method for allocating storage locations tovariables while compiling code for a computing system, comprising:identifying a first variable associated with a code segment within codebeing compiled; assigning a first priority tag to the first variable;identifying a second variable associated with another code segmentwithin the code being compiled; assigning a second priority tag to thesecond variable; using the assigned priority tags in assigning storagelocations to the first and second variables; wherein using the assignedpriority tags in assigning storage locations to the first and secondvariables comprises: determining whether the first and second variableare contemporaneously live during execution of the compiled code;determining whether legal storage location sets for the first and secondvariables overlap when it is determined that the first and secondvariable are contemporaneously live during execution of the compiledcode; comparing the priority tags assigned to each of the first andsecond variables when it is determined that the first and secondvariables are contemporaneously live during execution of the compiledcode and have overlapping legal storage location sets; and subtracting,when the first and second variables have different priority tags, thelegal storage location set of the higher priority variable from thelegal storage location set of the lower priority variable to obtain aremainder set of storage locations; determining whether the remainderset of storage locations is empty; assigning the remainder set ofstorage locations to the variable with the lower priority tag as a newlegal parameter set and proceeding with compiler operations when theremainder storage location set is not empty; and inserting aninterference edge in an interference graph and proceeding with thecompiler operations when the remainder set of storage locations isempty.
 2. The method of claim 1, further comprising: inserting aninterference edge in an interference graph and proceeding with compileroperations when the first and second variables both have low prioritytags.
 3. The method of claim 1, further comprising: determining anintersection set of legal storage locations common to both the first andsecond variables when the first and second variables both have highpriority tags; and partitioning the intersection set of legal storagelocations approximately equally between the first and second variablesinto a first partition set for the first variable and a second partitionset for the second variable.
 4. The method of claim 3, furthercomprising: subtracting the first partition set from the legal partitionset of the second variable to obtain a first remainder set; subtractingthe second partition set from the legal partition set of the firstvariable to obtain a second remainder set; determining whether the firstremainder set is empty; and determining whether the second remainder setis empty.
 5. The method of claim 3, further comprising: inserting aninterference edge in an interference graph and proceeding with compileroperations when either of the first or second remainder sets is empty.6. The method of claim 4, further comprising: assigning the firstremainder set to the first variable as a new legal storage location set;assigning the second remainder set to the first variable as another newlegal storage location set; and proceeding with compiler operations whenboth of the first and second remainder sets are not empty.
 7. The methodof claim 1, wherein identifying a first variable associated with a codesegment within code being compiled comprises identifying a firstvariable associated with a code segment within code being compiled by aruntime compiler.
 8. The method of claim 1, wherein identifying a firstvariable associated with a code segment within code being compiledcomprises identifying a first variable associated with a code segmentwithin code being compiled by a static compiler.
 9. A computing deviceconfigured to allocate storage locations to variables while compilingcode, comprising: a memory; a processor; means for identifying a firstvariable associated with a code segment within code being compiled;means for assigning a first priority tag to the first variable; meansfor identifying a second variable associated with another code segmentwithin the code being compiled; means for assigning a second prioritytag to the second variable; means for using the assigned priority tagsin assigning storage locations to the first and second variables;wherein means for using the assigned priority tags in assigning storagelocations to the first and second variables comprises: means fordetermining whether the first and second variable are contemporaneouslylive during execution of the compiled code; means for determiningwhether legal storage location sets for the first and second variablesoverlap when it is determined that the first and second variable arecontemporaneously live during execution of the compiled code; means forcomparing the priority tags assigned to each of the first and secondvariables when it is determined that the first and second variables arecontemporaneously live during execution of the compiled code and haveoverlapping legal storage location sets; and means for subtracting, whenthe first and second variables have different priority tags, the legalstorage location set of the higher priority variable from the legalstorage location set of the lower priority variable to obtain aremainder set of storage locations; means for determining whether theremainder set of storage locations is empty; means for assigning theremainder set of storage locations to the variable with the lowerpriority tag as a new legal parameter set and proceeding with compileroperations when the remainder set of storage locations is not empty; andmeans for inserting an interference edge in an interference graph andproceeding with the compiler operations when the remainder set ofstorage locations is empty.
 10. The computing device of claim 9, furthercomprising: means for inserting an interference edge in an interferencegraph and proceeding with compiler operations when the first and secondvariables both have low priority tags.
 11. The computing device of claim9, further comprising: means for determining an intersection set oflegal storage locations common to both the first and second variableswhen the first and second variables both have high priority tags; andmeans for partitioning the intersection set of legal storage locationsapproximately equally between the first and second variables into afirst partition set for the first variable and a second partition setfor the second variable.
 12. The computing device of claim 11, furthercomprising: means for subtracting the first partition set from the legalpartition set of the second variable to obtain a first remainder set;means for subtracting the second partition set from the legal partitionset of the first variable to obtain a second remainder set; means fordetermining whether the first remainder set is empty; and means fordetermining whether the second remainder set is empty.
 13. The computingdevice of claim 12, further comprising: means for inserting aninterference edge in an interference graph and proceeding with compileroperations when either of the first or second remainder sets is empty.14. The computing device of claim 12, further comprising: means forassigning the first remainder set to the first variable as a new legalstorage location set; means for assigning the second remainder set tothe first variable as another new legal storage location set; and meansfor proceeding with compiler operations when both of the first andsecond remainder sets are not empty.
 15. The computing device of claim9, wherein means for identifying a first variable associated with a codesegment within code being compiled comprises means for identifying afirst variable associated with a code segment within code being compiledby a runtime compiler.
 16. The computing device of claim 9, whereinmeans for identifying a first variable associated with a code segmentwithin code being compiled comprises means for identifying a firstvariable associated with a code segment within code being compiled by astatic compiler.
 17. A non-transitory computer readable storage mediumhaving stored thereon processor-executable software instructionsconfigured to cause a processor to perform operations for allocatingstorage locations to variables while compiling code, the operationscomprising: identifying a first variable associated with a code segmentwithin code being compiled; assigning a first priority tag to the firstvariable; identifying a second variable associated with another codesegment within the code being compiled; assigning a second priority tagto the second variable; and using the assigned priority tags inassigning storage locations to the first and second variables; whereinusing the assigned priority tags in assigning storage locations to thefirst and second variables comprises: determining whether the first andsecond variable are contemporaneously live during execution of thecompiled code; determining whether legal storage location sets for thefirst and second variables overlap when it is determined that the firstand second variable are contemporaneously live during execution of thecompiled code; comparing the priority tags assigned to each of the firstand second variables when it is determined that the first and secondvariables are contemporaneously live during execution of the compiledcode and have overlapping legal storage location sets; and subtracting,when the first and second variables have different priority tags, thelegal storage location set of the higher priority variable from thelegal storage location set of the lower priority variable to obtain aremainder set of storage locations; determining whether the remainderset of storage locations is empty; assigning the remainder set ofstorage locations to the variable with the lower priority tag as a newlegal parameter set and proceeding with compiler operations when theremainder set of storage locations is not empty; and inserting aninterference edge in an interference graph and proceeding with thecompiler operations when the remainder set of storage locations isempty.
 18. The non-transitory computer readable storage medium of claim17, wherein the stored processor-executable instructions are configuredto cause a processor to perform operations further comprising: insertingan interference edge in an interference graph and proceeding withcompiler operations when the first and second variables both have lowpriority tags.
 19. The non-transitory computer readable storage mediumof claim 17, wherein the stored processor-executable instructions areconfigured to cause a processor to perform operations furthercomprising: determining an intersection set of legal storage locationscommon to both the first and second variables when the first and secondvariables both have high priority tags; and partitioning theintersection set of legal storage locations approximately equallybetween the first and second variables into a first partition set forthe first variable and a second partition set for the second variable.20. The non-transitory computer readable storage medium of claim 19,wherein the stored processor-executable instructions are configured tocause a processor to perform operations further comprising: subtractingthe first partition set from the legal partition set of the secondvariable to obtain a first remainder set; subtracting the secondpartition set from the legal partition set of the first variable toobtain a second remainder set; determining whether the first remainderset is empty; and determining whether the second remainder set is empty.21. The non-transitory computer readable storage medium of claim 20,wherein the processor is configured with processor-executableinstructions to perform operations further comprising: inserting aninterference edge in an interference graph and proceeding with compileroperations when either of the first or second remainder sets is empty.22. The non-transitory computer readable storage medium of claim 20,wherein the stored processor-executable instructions are configured tocause a processor to perform operations further comprising: assigningthe first remainder set to the first variable as a new legal storagelocation set; assigning the second remainder set to the first variableas another new legal storage location set; and proceeding with compileroperations when both of the first and second remainder sets are notempty.
 23. The non-transitory computer readable storage medium of claim17, wherein the stored processor-executable instructions are configuredto cause a processor to perform operations such that identifying a firstvariable associated with a code segment within code being compiledcomprises identifying a first variable associated with a code segmentwithin code being compiled by a runtime compiler.
 24. The non-transitorycomputer readable storage medium of claim 17, wherein the storedprocessor-executable instructions are configured to cause a processor toperform operations such that identifying a first variable associatedwith a code segment within code being compiled comprises identifying afirst variable associated with a code segment within code being compiledby a static compiler.
 25. A computing device, comprising: a memory; anda processor coupled to the computing device and the memory, wherein theprocessor is configured with processor-executable instructions toperform operations comprising: identifying a first variable associatedwith a code segment within code being compiled; assigning a firstpriority tag to the first variable; identifying a second variableassociated with another code segment within the code being compiled;assigning a second priority tag to the second variable; using theassigned priority tags in assigning storage locations to the first andsecond variables; wherein using the assigned priority tags in assigningstorage locations to the first and second variables comprises:determining whether the first and second variable are contemporaneouslylive during execution of the compiled code; determining whether legalstorage location sets for the first and second variables overlap when itis determined that the first and second variable are contemporaneouslylive during execution of the compiled code; comparing the priority tagsassigned to each of the first and second variables when it is determinedthat the first and second variables are contemporaneously live duringexecution of the compiled code and have overlapping legal storagelocation sets; and subtracting, when the first and second variables havedifferent priority tags, the legal storage location set of the higherpriority variable from the legal storage location set of the lowerpriority variable to obtain a remainder set of storage locations;determining whether the remainder set of storage locations is empty;assigning the remainder set of storage locations to the variable withthe lower priority tag as a new legal parameter set and proceeding withcompiler operations when the remainder set of storage locations is notempty; and inserting an interference edge in an interference graph andproceeding with the compiler operations when the remainder set ofstorage locations is empty.
 26. The computing device of claim 25,wherein the processor is configured with processor-executableinstructions to perform operations further comprising: inserting aninterference edge in an interference graph and proceeding with compileroperations when the first and second variables both have low prioritytags.
 27. The computing device of claim 25, wherein the processor isconfigured with processor-executable instructions to perform operationsfurther comprising: determining an intersection set of legal storagelocations common to both the first and second variables when the firstand second variables both have high priority tags; and partitioning theintersection set of legal storage locations approximately equallybetween the first and second variables into a first partition set forthe first variable and a second partition set for the second variable.28. The computing device of claim 27, wherein the processor isconfigured with processor-executable instructions to perform operationsfurther comprising: subtracting the first partition set from the legalpartition set of the second variable to obtain a first remainder set;subtracting the second partition set from the legal partition set of thefirst variable to obtain a second remainder set; determining whether thefirst remainder set is empty; and determining whether the secondremainder set is empty.
 29. The computing device of claim 28, whereinthe processor is configured with processor-executable instructions toperform operations further comprising: inserting an interference edge inan interference graph and proceeding with compiler operations wheneither of the first or second remainder sets is empty.
 30. The computingdevice of claim 28, wherein the processor is configured withprocessor-executable instructions to perform operations furthercomprising: assigning the first remainder set to the first variable as anew legal storage location set; assigning the second remainder set tothe first variable as another new legal storage location set; andproceeding with compiler operations when both of the first and secondremainder sets are not empty.
 31. The computing device of claim 25,wherein the processor is configured with processor-executableinstructions such that identifying a first variable associated with acode segment within code being compiled comprises identifying a firstvariable associated with a code segment within code being compiled by aruntime compiler.
 32. The computing device of claim 25, wherein theprocessor is configured with processor-executable instructions such thatidentifying a first variable associated with a code segment within codebeing compiled comprises identifying a first variable associated with acode segment within code being compiled by a static compiler.